U.S. patent application number 11/514411 was filed with the patent office on 2007-01-04 for method for optimizing the location of a secondary cutting structure component in a drill string.
This patent application is currently assigned to Smith International, Inc.. Invention is credited to Luis C. Paez.
Application Number | 20070005316 11/514411 |
Document ID | / |
Family ID | 38616919 |
Filed Date | 2007-01-04 |
United States Patent
Application |
20070005316 |
Kind Code |
A1 |
Paez; Luis C. |
January 4, 2007 |
Method for optimizing the location of a secondary cutting structure
component in a drill string
Abstract
A method of drilling a well using at least one drill bit and at
least one secondary cutting structure, that includes determining a
neutral point of a drill string positioning at least one secondary
cutting structure based on the neutral point of the drill string,
and drilling an earth formation.
Inventors: |
Paez; Luis C.; (The
Woodlands, TX) |
Correspondence
Address: |
OSHA, LIANG LLP / SMITH
1221 MCKINNEY STREET
SUITE 2800
HOUSTON
TX
77010
US
|
Assignee: |
Smith International, Inc.
Houston
TX
77032
|
Family ID: |
38616919 |
Appl. No.: |
11/514411 |
Filed: |
September 1, 2006 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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11137713 |
May 25, 2005 |
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11514411 |
Sep 1, 2006 |
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11365065 |
Feb 28, 2006 |
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11514411 |
Sep 1, 2006 |
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11100337 |
Apr 6, 2005 |
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11514411 |
Sep 1, 2006 |
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Current U.S.
Class: |
703/10 |
Current CPC
Class: |
E21B 10/43 20130101;
E21B 10/46 20130101; E21B 44/00 20130101; E21B 7/04 20130101; E21B
10/00 20130101; E21B 7/00 20130101 |
Class at
Publication: |
703/010 |
International
Class: |
G06G 7/48 20060101
G06G007/48 |
Claims
1. A method of determining an improved position of a secondary
cutting structure used in a drilling tool assembly, comprising:
determining a neutral point of the drilling tool assembly; modeling
the drilling tool assembly having at least one secondary cutting
structure at a first position; simulating the drilling tool
assembly; moving a location of the at least one secondary cutting
structure closer to the neutral point of the drilling tool
assembly; simulating the drilling tool assembly; and determining a
location for the at least one secondary cutting structure based on
the simulating.
2. The method of claim 1, wherein simulating the drilling tool
assembly comprises outputting a graphical display of at least one
of a lateral acceleration, torque on bit, torque or reamer, surface
torque, rate of penetration, and a bending moment.
3. The method of claim 1, further comprising drilling a well with
at least one drill bit and a secondary cutting structure located
adjacent to the determined location.
4. The method of claim 1, wherein the at least one secondary
cutting structure comprises a reamer.
5. The method of claim 1, wherein a determined location for the at
least one secondary cutting structure is within 50 feet of the
neutral point.
6. The method of claim 5, wherein the determined location for the
at least one secondary cutting structure is within 5 feet of the
neutral point.
7. A method of drilling a well using at least one drill bit and at
least one secondary cutting structure, comprising: determining a
neutral point of a drill string; positioning at least one secondary
cutting structure based on the neutral point of the drill string;
and drilling an earth formation.
8. The method of claim 7, wherein the positioning comprises placing
the at least one secondary cutting structure within 60 feet of the
neutral point.
9. The method of claim 8, wherein the positioning comprises placing
the at least one secondary cutting structure within 30 feet of the
neutral point.
10. The method of claim 9, wherein the positioning comprises
placing the at least one secondary cutting structure within 10 feet
of the neutral point.
11. A method of selecting a weight on bit for a drilling
application, comprising: determining, for a given drill string
design, a neutral point based on a first weight on bit;
determining; for the given drill string design, a neutral point
based on a second weight on bit; selecting a weight on bit, based
on the first and second weight on bits, that places the neutral
point of the drill string adjacent a secondary cutting structure.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application claims the benefit, pursuant to 35 U.S.C.
.sctn. 120, as a continuation-in-part application of U.S. patent
application Ser. Nos. 11/100,337, 11/137,713, and 11/365,065, all
of which are expressly incorporated by reference in their
entirety.
[0002] Further, this application also expressly incorporates the
additional following references by reference in their entirety:
Ser. Nos. 11/385,969, 09/524,088 (now U.S. Pat. No. 6,516,293),
Ser. No. 09/635,116 (now U.S. Pat. No. 6,873,947), Ser. Nos.
10/749,019, 09/689,299 (now U.S. Pat. No. 6,785,641), Ser. Nos.
10/852,574, 10/851,677, 10/888,358, and 10/888,446.
BACKGROUND OF INVENTION
[0003] 1. Field of the Invention
[0004] The invention relates generally to methods and systems
involving cutting tools in oilfield applications.
[0005] 2. Background Art
[0006] FIG. 1 shows one example of a conventional drilling system
for drilling an earth formation. The drilling system includes a
drilling rig 10 used to turn a drilling tool assembly 12 that
extends downward into a well bore 14. The drilling tool assembly 12
includes a drilling string 16, and a bottomhole assembly (BHA) 18,
which is attached to the distal end of the drill string 16. The
"distal end" of the drill string is the end furthest from the
drilling rig.
[0007] The drill string 16 includes several joints of drill pipe
16a connected end to end through tool joints 16b. The drill string
16 is used to transmit drilling fluid (through its hollow core) and
to transmit rotational power from the drill rig 10 to the BHA 18.
In some cases the drill string 16 further includes additional
components such as subs, pup joints, etc.
[0008] The BHA 18 includes at least a drill bit 20. Typical BHA's
may also include additional components attached between the drill
string 16 and the drill bit 20. Examples of additional BHA
components include drill collars, stabilizers,
measurement-while-drilling (MWD) tools, logging-while-drilling
(LWD) tools, subs, hole enlargement devices (e.g., hole openers and
reamers), jars, accelerators, thrusters, downhole motors, and
rotary steerable systems.
[0009] In general, drilling tool assemblies 12 may include other
drilling components and accessories, such as special valves, such
as kelly cocks, blowout preventers, and safety valves. Additional
components included in a drilling tool assembly 12 may be
considered a part of the drill string 16 or a part of the BHA 18
depending on their locations in the drilling tool assembly 12.
[0010] The drill bit 20 in the BHA 18 may be any type of drill bit
suitable for drilling earth formation. Two common types of drill
bits used for drilling earth formations are fixed-cutter (or
fixed-head) bits and roller cone bits. FIG. 2 shows one example of
a fixed-cutter bit. FIG. 3 shows one example of a roller cone
bit.
[0011] Referring to FIG. 2, fixed-cutter bits (also called drag
bits) 21 typically comprise a bit body 22 having a threaded
connection at one end 24 and a cutting head 26 formed at the other
end. The head 26 of the fixed-cutter bit 21 typically includes a
plurality of ribs or blades 28 arranged about the rotational axis
of the drill bit and extending radially outward from the bit body
22. Cutting elements 29 are embedded in the raised ribs 28 to cut
formation as the drill bit is rotated on a bottom surface of a well
bore. Cutting elements 29 of fixed-cutter bits typically comprise
polycrystalline diamond compacts (PDC) or specially manufactured
diamond cutters. These drill bits are also referred to as PDC
bits.
[0012] Referring to FIG. 3, roller cone bits 30 typically comprise
a bit body 32 having a threaded connection at one end 34 and one or
more legs (typically three) extending from the other end. A roller
cone 36 is mounted on each leg and is able to rotate with respect
to the bit body 32. On each cone 36 of the drill bit 30 are a
plurality of cutting elements 38, typically arranged in rows about
the surface of the cone 36 to contact and cut through formation
encountered by the drill bit. Roller cone bits 30 are designed such
that as a drill bit rotates, the cones 36 of the roller cone bit 30
roll on the bottom surface of the well bore (called the
"bottomhole") and the cutting elements 38 scrape and crush the
formation beneath them. In some cases, the cutting elements 38 on
the roller cone bit 30 comprise milled steel teeth formed on the
surface of the cones 36. In other cases, the cutting elements 38
comprise inserts embedded in the cones. Typically, these inserts
are tungsten carbide inserts or polycrystalline diamond compacts.
In some cases hardfacing is applied to the surface of the cutting
elements and/or cones to improve wear resistance of the cutting
structure.
[0013] For a drill bit 20 to drill through formation, sufficient
rotational moment and axial force must be applied to the drill bit
20 to cause the cutting elements of the drill bit 20 to cut into
and/or crush formation as the drill bit is rotated. The axial force
applied on the drill bit 20 is typically referred to as the "weight
on bit" (WOB). The rotational moment applied to the drilling tool
assembly 12 at the drill rig 10 (usually by a rotary table or a top
drive mechanism) to turn the drilling tool assembly 12 is referred
to as the "rotary torque". The speed at which the rotary table
rotates the drilling tool assembly 12, typically measured in
revolutions per minute (RPM), is referred to as the "rotary speed".
Additionally, the portion of the weight of the drilling tool
assembly supported at the rig 10 by the suspending mechanism (or
hook) is typically referred to as the hook load.
[0014] As the drilling industry continues to evolve, methods of
simulating and/or modeling the performance of components used in
the drilling industry have begun to be developed. Drilling tool
assemblies can extend more than a mile in length while being less
than a foot in diameter. As a result, these assemblies are
relatively flexible along their length and may vibrate when driven
rotationally by the rotary table. Drilling tool assembly vibrations
may also result from vibration of the drill bit during drilling.
Several modes of vibration are possible for drilling tool
assemblies. In general, drilling tool assemblies may experience
torsional, axial, and lateral vibrations. Although partial damping
of vibration may result due to viscosity of drilling fluid,
friction of the drill pipe rubbing against the wall of the well
bore, energy absorbed in drilling the formation, and drilling tool
assembly impacting with well bore wall, these sources of damping
are typically not enough to suppress vibrations completely.
[0015] One example of a method that may be used to simulate a
drilling tool assembly is disclosed in U.S. patent application Ser.
No. 09/689,299 entitled "Simulating the Dynamic Response of a
Drilling Tool Assembly and its Application to Drilling Tool
Assembly Design Optimizing and Drilling Performance Optimization",
which is incorporated by reference in its entirety.
[0016] Vibrations of a drilling tool assembly are difficult to
predict because different forces may combine to produce the various
modes of vibration, and models for simulating the response of an
entire drilling tool assembly including a drill bit interacting
with formation in a drilling environment have not been available.
Drilling tool assembly vibrations are generally undesirable, not
only because they are difficult to predict, but also because the
vibrations can significantly affect the instantaneous force applied
on the drill bit. This can result in the drill bit not operating as
expected.
[0017] For example, vibrations can result in off-centered drilling,
slower rates of penetration, excessive wear of the cutting
elements, or premature failure of the cutting elements and the
drill bit. Lateral vibration of the drilling tool assembly may be a
result of radial force imbalances, mass imbalance, and drill
bit/formation interaction, among other things. Lateral vibration
results in poor drilling tool assembly performance, overgage hole
drilling, out-of-round, or "lobed" well bores and premature failure
of both the cutting elements and drill bit bearings. Lateral
vibration is particularly problematic if hole openers are used.
[0018] During drilling operations, it may be desirable to increase
the diameter of the drilled wellbore to a selected larger diameter.
Further, increasing the diameter of the wellbore may be necessary
if, for example, the formation being drilled is unstable such that
the wellbore diameter changes after being drilled by the drill bit.
Accordingly, tools known in the art such as "hole openers" and
"underreamers" have been used to enlarge diameters of drilled
wellbores.
[0019] In some drilling environments, it may be advantageous, from
an ease of drilling standpoint, to drill a smaller diameter
borehole (e.g., an 81/2 inch diameter hole) before opening or
underreaming the borehole to a larger diameter (e.g., to a 171/2
inch diameter hole). Other circumstances in which first drilling
smaller hole and then underreaming or opening the hole include
directionally drilled boreholes. It is difficult to directionally
drill a wellbore with a large diameter bit because, for example,
larger diameter bits have an increased tendency to "torque-up" (or
stick) in the wellbore. When a larger diameter bit "torques-up",
the bit tends to drill a tortuous trajectory because it
periodically sticks and then frees up and unloads torque. Therefore
it is often advantageous to directionally drill a smaller diameter
hole before running a hole opener in the wellbore to increase the
wellbore to a desired larger diameter.
[0020] A typical prior art hole opener is disclosed in U.S. Pat.
No. 4,630,694 issued to Walton et al. The hole opener disclosed in
the '694 patent includes a bull nose, a pilot section, and an
elongated body adapted to be connected to a drillstring used to
drill a wellbore. The hole opener also includes a triangularly
arranged, hardfaced blade structure adapted to increase a diameter
of the wellbore.
[0021] Another prior art hole opener is disclosed in U.S. Pat. No.
5,035,293 issued to Rives. The hole opener disclosed in the '293
patent may be used either as a sub in a drill string, or may be
coupled to the bottom end of a drill string in a manner similar to
a drill bit. This particular hole opener includes radially spaced
blades with cutting elements and shock absorbers disposed
thereon.
[0022] Other prior art hole openers include, for example, rotatable
cutters affixed to a tool body in a cantilever fashion. Such a hole
opener is shown, for example, in U.S. Pat. No. 5,992,542 issued to
Rives. The hole opener disclosed in the '542 patent includes
hardfaced cutter shells that are similar to roller cones used with
roller cone drill bits.
[0023] U.S. Patent Publication No. 2004/0222025, which is assigned
to the assignee of the present invention, and is incorporated by
reference in its entirety, discloses a hole opener wherein cutting
elements may be positioned on the respective blades so as to
balance a force or work distribution and provide a force or work
balanced cutting structure. "Force balance" may refer to a
substantial balancing of any force during drilling (lateral, axial,
torsional, and/or vibrational, for example). One method of later
force balancing has been described in detail in, for example, T. M.
Warren et al., Drag Bit Performance Modeling, paper no. 15617,
Society of Petroleum Engineers, Richardson, Tex., 1986. Similarly,
"work balance" refers to a substantial balancing of work performed
between the blades and between cutting elements on the blades.
[0024] The term "work" used in that publication is defined as
follows. A cutting element on the blades during drilling operations
cuts the earth formation through a combination of axial penetration
and lateral scraping. The movement of the cutting element through
the formation can thus be separated into a "lateral scraping"
component and an "axial crushing" component. The distance that the
cutting element moves laterally, that is, in the plane of the
bottom of the wellbore, is called the lateral displacement. The
distance that the cutting element moves in the axial direction is
called the vertical displacement. The force vector acting on the
cutting element can also be characterized by a lateral force
component acting in the plane of the bottom of the wellbore and a
vertical force component acting along the axis of the drill bit.
The work done by a cutting element is defined as the product of the
force required to move the cutting element and the displacement of
the cutting element in the direction of the force.
[0025] Thus, the lateral work done by the cutting element is the
product of the lateral force and the lateral displacement.
Similarly, the vertical (axial) work done is the product of the
vertical force and the vertical displacement. The total work done
by each cutting element can be calculated by summing the vertical
work and the lateral work. Summing the total work done by each
cutting element on any one blade will provide the total work done
by that blade.
[0026] Force balancing and work balancing may also refer to a
substantial balancing of forces and work between corresponding
cutting elements, between redundant cutting elements, etc.
Balancing may also be performed over the entire hole opener (e.g.,
over the entire cutting structure).
[0027] What is still needed, however, are methods for determining
where to position secondary cutting structures such as reamers, or
other hole openers, and other tools on a drill string in order to
improve drilling performance.
SUMMARY OF INVENTION
[0028] In one aspect, the method of drilling a well using at least
one drill bit and at least one secondary cutting structure,
includes determining a neutral point of a drill string positioning
at least one secondary cutting structure based on the neutral point
of the drill string, and drilling an earth formation.
[0029] In another aspect, the method of determining an improved
position of a secondary cutting structure used in a drilling tool
assembly, includes determining a neutral point of the drilling tool
assembly, modeling the drilling tool assembly having at least one
secondary cutting structure at a first position, simulating the
drilling tool assembly, moving a location of the at least one
secondary cutting structure closer to the neutral point of the
drilling tool assembly, simulating the drilling tool assembly, and
determining a location for the at least one secondary cutting
structure based on the simulating.
[0030] Other aspects and advantages of the invention will be
apparent from the following description and the appended
claims.
BRIEF DESCRIPTION OF DRAWINGS
[0031] FIG. 1 shows a conventional drilling system for drilling an
earth formation.
[0032] FIG. 2 shows a conventional fixed-cutter bit.
[0033] FIG. 3 shows a conventional roller cone bit.
[0034] FIG. 4 shows a perspective view of an embodiment of the
invention.
[0035] FIG. 5 shows a flow chart of one embodiment of a method for
simulating the dynamic response of a drilling tool assembly.
[0036] FIG. 6 shows a flow chart of one embodiment of a method of
incrementally solving for the dynamic response of a drilling tool
assembly.
[0037] FIG. 7 shows a more detailed flow chart of one embodiment of
a method for incrementally solving for the dynamic response of a
drilling tool assembly.
[0038] FIG. 8 shows a bit in accordance with an embodiment of the
invention.
[0039] FIG. 9 shows a bit in accordance with an embodiment of the
invention.
[0040] FIGS. 10A-10B show primary and secondary cutter tip profiles
in accordance with an embodiment of the invention.
[0041] FIG. 11 is a cross sectional elevation view of one
embodiment of the expandable tool of the present invention, showing
the moveable arms in the collapsed position.
[0042] FIG. 12 is a cross-sectional elevation view of the
expandable tool of FIG. 11, showing the moveable arms in the
expanded position.
[0043] FIG. 13 shows a flow chart in accordance with one embodiment
of the present invention.
[0044] FIG. 14 shows a chart of lateral acceleration against reamer
position in accordance with one embodiment of the present
invention.
[0045] FIGS. 15A-D show charts of torque on the reamer against
reamer position in accordance with one embodiment of the present
invention.
[0046] FIG. 16 shows a comparison of torque on the system against
reamer position in accordance with one embodiment of the present
invention.
[0047] FIG. 17 shows a chart of rate of penetration against reamer
position in accordance with one embodiment of the present
invention.
[0048] FIG. 18 shows a chart of bending moment at an MWD tool
against reamer position in accordance with one embodiment of the
present invention.
DETAILED DESCRIPTION
[0049] The present invention relates to a provide techniques for
locating secondary cutting structures (such as hole openers) in a
drill string. Specifically, selected embodiments involve
determining (whether by calculating or by other means) a neutral
point of a drilling system, and positioning a secondary cutting
structure adjacent to the neutral point of the drilling system.
[0050] FIG. 4 shows a general configuration of a hole opener 430
that may be used in embodiments of the present invention. The hole
opener 430 includes a tool body 432 and a plurality of blades 438
disposed at selected azimuthal locations about a circumference
thereof. The hole opener 430 generally comprises connections 434,
436 (e.g., threaded connections) so that the hole opener 430 may be
coupled to adjacent drilling tools that comprise, for example, a
drillstring and/or bottom hole assembly (BHA) (not shown). The tool
body 432 generally includes a bore 35 therethrough so that drilling
fluid may flow through the hole opener 430 as it is pumped from the
surface (e.g., from surface mud pumps (not shown)) to a bottom of
the wellbore (not shown). The tool body 432 may be formed from
steel or from other materials known in the art. For example, the
tool body 432 may also be formed from a matrix material infiltrated
with a binder alloy.
[0051] The blades 438 shown in FIG. 4 are spiral blades and are
generally positioned asymmetrically at substantially equal angular
intervals about the perimeter of the tool body 432 so that the hole
opener 430 will be positioned substantially concentric with the
wellbore (not shown) during drilling operations (e.g., a
longitudinal axis 437 of the well opener 430 will remain
substantially coaxial with a longitudinal axis of the wellbore (not
shown)). Alternatively, the hole opener may be eccentric.
[0052] Other blade arrangements may be used with the invention, and
the embodiment shown in FIG. 4 is not intended to limit the scope
of the invention. For example, the blades 438 may be positioned
symmetrically about the perimeter of the tool body 432 at
substantially equal angular intervals so long as the hole opener
430 remains positioned substantially concentric with the wellbore
(not shown) during drilling operations. Moreover, the blades 438
may be straight instead of spiral.
[0053] The blades 438 each typically include a plurality of cutting
elements 440 disposed thereon, and the blades 438 and the cutting
elements 440 generally form a cutting structure 431 of the hole
opener 430. The cutting elements 440 may be, for example,
polycrystalline diamond compact (PDC) inserts, tungsten carbide
inserts, boron nitride inserts, and other similar inserts known in
the art. The cutting elements 440 are generally arranged in a
selected manner on the blades 438 so as to drill a wellbore having
a larger diameter than, for example, a diameter of a wellbore (not
shown) previously drilled with a drill bit. For example, FIG. 4
shows the cutting elements 440 arranged in a manner so that a
diameter subtended by the cutting elements 440 gradually increases
with respect to an axial position of the cutting elements 440 along
the blades 438 (e.g., with respect to an axial position along the
hole opener 430). Note that the subtended diameter may be selected
to increase at any rate along a length of the blades 438 so as to
drill a desired increased diameter wellbore (not shown).
[0054] In other embodiments, the blades 438 may be formed from a
diamond impregnated material. In such embodiments, the diamond
impregnated material of the blades 438 effectively forms the
cutting structure 431. Moreover, such embodiments may also have
gage protection elements as described below. Accordingly,
embodiments comprising cutting elements are not intended to limit
the scope of the invention.
[0055] The hole opener 430 also generally includes tapered surfaces
444 formed proximate a lower end of the blades 438. The tapered
surfaces 444 comprise a lower diameter 443 that may be, for
example, substantially equal to a diameter 441 of the tool body
432. However, in other embodiments, the lower diameter 443 may be
larger than the diameter 441 of the tool body 432. The tapered
surfaces 444 also comprise an upper diameter 445 that may, in some
embodiments, be substantially equal to a diameter of the wellbore
(not shown) drilled by a drill bit (not shown) positioned below the
hole opener 430 in the drillstring (not shown). In other
embodiments, the upper diameter 445 may be selected so as to be
less than the diameter of the wellbore (not shown) drilled by the
drill bit (not shown). Note that the tapered surfaces are not
intended to be limiting.
[0056] In some embodiments, the tapered surfaces 444 may also
include at least one cutting element disposed thereon. As described
above, the cutting elements may comprise polycrystalline diamond
compact (PDC) inserts, tungsten carbide inserts, boron nitride
inserts, and other similar inserts known in the art. The cutting
elements may be selectively positioned on the tapered surfaces 444
so as to drill out an existing pilot hole (not shown) if, for
example, an existing pilot hole (not shown) is undersize.
[0057] The hole opener 430 also comprises gage surfaces 446 located
proximate an upper end of the blades 438. The gage surfaces 446
shown in the embodiment of FIG. 4 are generally spiral gage
surfaces formed on an upper portion of the spiral blades 438.
However, other embodiments may comprise substantially straight gage
surfaces.
[0058] In other embodiments, the cutting elements 440 may comprise
different diameter cutting elements. For example, 13 mm cutting
elements are commonly used with PDC drill bits. The cutting
elements disposed on the blades 438 may comprise, for example, 9
mm, 11 mm, 13 mm, 16 mm, 19 mm, 22 mm, and/or 25 mm cutters, among
other diameters. Further, different diameter cutting elements may
be used on a single blade (e.g., the diameter of cutting elements
maybe selectively varied along a length of a blade).
[0059] In another aspect of the invention, the cutting elements 440
may be positioned at selected backrake angles. A common backrake
angle used in, for example, prior art PDC drill bits is
approximately 20 degrees. However, the cutting elements in various
embodiments according to this aspect of the invention may be
positioned at backrake angles of greater than or less than 20
degrees. Moreover, the backrake angle of the cutting elements may
be varied on the same blade or bit. In one embodiment, the backrake
angle is variable along the length of the blade. In a particular
embodiment, the backrake angle of each cutting element is related
to the axial position of the particular cutting element along the
length of the blade.
[0060] In some embodiments, the blades 438 and/or other portions of
the cutting structure 431 may be formed from a non-magnetic
material such as monel. In other embodiments, the blades 438 and/or
other portions of the cutting structure 431 may be formed from
materials that include a matrix infiltrated with binder materials.
Examples of these infiltrated materials may be found in, for
example, U.S. Pat. No. 4,630,692 issued to Ecer and U.S. Pat. No.
5,733,664 issued to Kelley et al. Such materials are advantageous
because they are highly resistant to erosive and abrasive wear, yet
are tough enough to withstand shock and stresses associated with
harsh drilling conditions.
[0061] Exemplary drill bits for use with embodiments of the present
invention are shown in FIGS. 2 and 3. Examples of simulation
methods for drill bits are provided in U.S. Pat. No. 6,516,293,
entitled "Method for Simulating Drilling of Roller Cone Bits and
its Application to Roller Cone Bit Design and Performance," and
U.S. Provisional Application No. 60/485,642, filed Jul. 9, 2003 and
entitled "Methods for Modeling, Designing, and Optimizing Fixed
Cutter Bits," which are both assigned to the assignee of the
present invention and now incorporated herein by reference in their
entirety.
[0062] As noted above, embodiments of the present invention build
upon the simulation techniques disclosed in the incorporated drill
bit patents and patent applications to couple the cutting action of
other cutting tools in a BHA.
Method of Dynamically Simulating Bit/Cutting Tool/BHA
[0063] A flow chart for one embodiment of the invention is
illustrated in FIG. 5. The first step in this embodiment is
selecting (defining or otherwise providing) in part parameters 100,
including initial drilling tool assembly parameters 102, initial
drilling environment parameters 104, drilling operating parameters
106, and drilling tool assembly/drilling environment interaction
information (parameters and/or models) 108. The step involves
constructing a mechanics analysis model of the drilling tool
assembly 110. The mechanics analysis model can be constructed using
the drilling tool assembly parameters 102 and Newton's law of
motion. The next step involves determining an initial static state
of the drilling tool assembly 112 in the selected drilling
environment using the mechanics analysis model 110 along with
drilling environment parameters 104 and drilling tool
assembly/drilling environment interaction information 108.
[0064] Once the mechanics analysis model is constructed and an
initial static state of the drill string is determined, the
resulting static state parameters can be used with the drilling
operating parameters 106 to incrementally solve for the dynamic
response 114 of the drilling tool assembly to rotational input from
the rotary table and the hook load provided at the hook. Once a
simulated response for an increment in time (or for the total time)
is obtained, results from the simulation can be provided as output
118, and used to generate a visual representation of drilling if
desired.
[0065] In one example, illustrated in FIG. 6, incrementally solving
for the dynamic response (indicated as 116) may not only include
solving the mechanics analysis model for the dynamic response to an
incremental rotation, at 120, but may also include determining,
from the response obtained, loads (e.g., drilling environment
interaction forces) on the drilling tool assembly due to
interaction between the drilling tool assembly and the drilling
environment during the incremental rotation, at 122, and resolving
for the response of the drilling tool assembly to the incremental
rotation, at 124, under the newly determined loads. The determining
and resolving may be repeated in a constraint update loop 128 until
a response convergence criterion 126 is satisfied. Once a
convergence criterion is satisfied, the entire incremental solving
process 116 may be repeated for successive increments until an end
condition for simulation is reached.
[0066] During the simulation, the constraint forces initially used
for each new incremental calculation step may be the constraint
forces determined during the last incremental rotation. In the
simulation, incremental rotation calculations are repeated for a
select number of successive incremental rotations until an end
condition for simulation is reached. A more detailed example of an
embodiment of the invention is shown in FIG. 7
[0067] For the example shown in FIG. 7, the parameters provided as
input (initial conditions) 200 include drilling tool assembly
design parameters 202, initial drilling environment parameters 204,
drilling operating parameters 206, and drilling tool
assembly/drilling environment interaction parameters and/or models
208.
[0068] Drilling tool assembly design parameters 202 may include
drill string design parameters, BHA design parameters, cutting tool
parameters, and drill bit design parameters. In the example shown,
the drill string comprises a plurality of joints of drill pipe, and
the BHA comprises drill collars, stabilizers, bent housings, and
other downhole tools (e.g., MWD tools, LWD tools, downhole motor,
etc.), and a drill bit. As noted above, while the drill bit,
generally, is considered a part of the BHA, in this example the
design parameters of the drill bit are shown separately to
illustrate that any type of drill bit may be defined and modeled
using any drill bit analysis model.
[0069] Drill string design parameters include, for example, the
length, inside diameter (ID), outside diameter (OD), weight (or
density), and other material properties of the drill string in the
aggregate. Alternatively, drill string design parameters may
include the properties of each component of the drill string and
the number of components and location of each component of the
drill string. For example, the length, ID, OD, weight, and material
properties of one joint of drill pipe may be provided along with
the number of joints of drill pipe which make up the drill string.
Material properties used may include the type of material and/or
the strength, elasticity, and density of the material. The weight
of the drill string, or individual components of the drill string
may be provided as "weight in drilling fluids" (the weight of the
component when submerged in the selected drilling fluid).
[0070] BHA design parameters include, for example, the bent angle
and orientation of the motor, the length, equivalent inside
diameter (ID), outside diameter (OD), weight (or density), and
other material properties of each of the various components of the
BHA. In this example, the drill collars, stabilizers, and other
downhole tools are defined by their lengths, equivalent IDs, ODs,
material properties, weight in drilling fluids, and position in the
drilling tool assembly.
[0071] Cutting tool design parameters include, for example, the
material properties and the geometric parameters of the cutting
tool. Geometric parameters of the cutting tool may include size of
the tool, number of blades, location of blades, expandable nature,
number of cutting elements, and the location, shape, size, and
orientation of the cutting elements.
[0072] The drill bit design parameters include, for example, the
bit type (roller cone, fixed-cutter, etc.) and geometric parameters
of the bit. Geometric parameters of the bit may include the bit
size (e.g., diameter), number of cutting elements, and the
location, shape, size, and orientation of the cutting elements. In
the case of a roller cone bit, drill bit design parameters may
further include cone profiles, cone axis offset (offset from
perpendicular with the bit axis of rotation), the number of cutting
elements on each cone, the location, size, shape, orientation, etc.
of each cutting element on each cone, and any other bit geometric
parameters (e.g., journal angles, element spacings, etc.) to
completely define the bit geometry. In general, bit, cutting
element, and cone geometry may be converted to coordinates and
provided as input. One preferred method for obtaining bit design
parameters is the use of 3-dimensional CAD solid or surface models
to facilitate geometric input. Drill bit design parameters may
further include material properties, such as strength, hardness,
etc. of components of the bit.
[0073] Initial drilling environment parameters 204 include, for
example, wellbore parameters. Wellbore parameters may include
wellbore trajectory (or geometric) parameters and wellbore
formation parameters. Wellbore trajectory parameters may include an
initial wellbore measured depth (or length), wellbore diameter,
inclination angle, and azimuth direction of the wellbore
trajectory. In the typical case of a wellbore comprising segments
having different diameters or differing in direction, the wellbore
trajectory information may include depths, diameters, inclination
angles, and azimuth directions for each of the various segments.
Wellbore trajectory information may further include an indication
of the curvature of the segments (which may be used to determine
the order of mathematical equations used to represent each
segment). Wellbore formation parameters may include the type of
formation being drilled and/or material properties of the formation
such as the formation strength, hardness, plasticity, and elastic
modulus.
[0074] Those skilled in the art will appreciate that any drill
string design parameter may be adjusted in the model. Moreover, in
selected embodiments of the model, the assembly may be considered
to be segmented into a primary cutting tool, first BHA segment,
secondary cutting tool, second BHA segment, etc.
[0075] Drilling operating parameters 206, in this embodiment,
include the rotary table speed at which the drilling tool assembly
is rotated (RPM), the downhole motor speed if a downhole motor is
included, and the hook load. Drilling operating parameters 206 may
further include drilling fluid parameters, such as the viscosity
and density of the drilling fluid, for example. It should be
understood that drilling operating parameters 206 are not limited
to these variables. In other embodiments, drilling operating
parameters 206 may include other variables, such as, for example,
rotary torque and drilling fluid flow rate. Additionally, drilling
operating parameters 206 for the purpose of simulation may further
include the total number of bit revolutions to be simulated or the
total drilling time desired for simulation. However, it should be
understood that total revolutions and total drilling time are
simply end conditions that can be provided as input to control the
stopping point of simulation, and are not necessary for the
calculation required for simulation. Additionally, in other
embodiments, other end conditions may be provided, such as total
drilling depth to be simulated, or by operator command, for
example.
[0076] Drilling tool assembly/drilling environment interaction
information 208 includes, for example, cutting element/earth
formation interaction models (or parameters) and drilling tool
assembly/formation impact, friction, and damping models and/or
parameters. Cutting element/earth formation interaction models may
include vertical force-penetration relations and/or parameters
which characterize the relationship between the axial force of a
selected cutting element on a selected formation and the
corresponding penetration of the cutting element into the
formation. Cutting element/earth formation interaction models may
also include lateral force-scraping relations and/or parameters
which characterize the relationship between the lateral force of a
selected cutting element on a selected formation and the
corresponding scraping of the formation by the cutting element.
[0077] Cutting element/formation interaction models may also
include brittle fracture crater models and/or parameters for
predicting formation craters which will likely result in brittle
fracture, wear models and/or parameters for predicting cutting
element wear resulting from contact with the formation, and cone
shell/formation or bit body/formation interaction models and/or
parameters for determining forces on the bit resulting from cone
shell/formation or bit body/formation interaction. One example of
methods for obtaining or determining drilling tool
assembly/formation interaction models or parameters can be found in
the previously noted U.S. Pat. No. 6,516,293, assigned to the
assignee of the present invention and incorporated herein by
reference. Other methods for modeling drill bit interaction with a
formation can be found in the previously noted SPE Papers No.
29922, No. 15617, and No. 15618, and PCT International Publication
Nos. WO 00/12859 and WO 00/12860.
[0078] Drilling tool assembly/formation impact, friction, and
damping models and/or parameters characterize impact and friction
on the drilling tool assembly due to contact with the wall of the
wellbore and the viscous damping effects of the drilling fluid.
These models/parameters include, for example, drill
string-BHA/formation impact models and/or parameters, bit
body/formation impact models and/or parameters, drill
string-BHA/formation friction models and/or parameters, and
drilling fluid viscous damping models and/or parameters. One
skilled in the art will appreciate that impact, friction and
damping models/parameters may be obtained through laboratory
experimentation, in a method similar to that disclosed in the prior
art for drill bits interaction models/parameters. Alternatively,
these models may also be derived based on mechanical properties of
the formation and the drilling tool assembly, or may be obtained
from literature. Prior art methods for determining impact and
friction models are shown, for example, in papers such as the one
by Yu Wang and Matthew Mason, entitled "Two-Dimensional Rigid-Body
Collisions with Friction", Journal of Applied Mechanics, September
1992, Vol. 59, pp. 635-642.
[0079] As shown in FIGS. 6-7, once input parameters/models 200 are
selected, determined, or otherwise provided, a multi-part mechanics
analysis model of the drilling tool assembly is constructed (at
210) and used to determine the initial static state (at 112 in FIG.
6) of the drilling tool assembly in the wellbore. The first part of
the mechanics analysis model 212 takes into consideration the
overall structure of the drilling tool assembly, with the drill
bit, and any cutting tools being only generally represented.
[0080] In this embodiment, for example, a finite element method may
be used wherein an arbitrary initial state (such as hanging in the
vertical mode free of bending stresses) is defined for the drilling
tool assembly as a reference and the drilling tool assembly is
divided into N elements of specified element lengths (i.e.,
meshed). The static load vector for each element due to gravity is
calculated.
[0081] Then element stiffness matrices are constructed based on the
material properties (e.g., elasticity), element length, and cross
sectional geometrical properties of drilling tool assembly
components provided as input and are used to construct a stiffness
matrix, at 212, for the entire drilling tool assembly (wherein the
drill bit may be generally represented by a single node).
Similarly, element mass matrices are constructed by determining the
mass of each element (based on material properties, etc.) and are
used to construct a mass matrix, at 214, for the entire drilling
tool assembly.
[0082] Additionally, element damping matrices can be constructed
(based on experimental data, approximation, or other method) and
used to construct a damping matrix, at 216, for the entire drilling
tool assembly. Methods for dividing a system into finite elements
and constructing corresponding stiffness, mass, and damping
matrices are known in the art and thus are not explained in detail
here. Examples of such methods are shown, for example, in "Finite
Elements for Analysis and Design" by J. E. Akin (Academic Press,
1994).
[0083] Furthermore, it will be noted that spaces between a
secondary cutting structure (hole opener for example) and a bit may
be accurately modeled.
[0084] The second part 217 of the mechanics analysis model 210 of
the drilling tool assembly is a mechanics analysis model of the at
least one cutting tool 217, which takes into account details of one
or more cutting tools. The cutting tool mechanics analysis model
217 may be constructed by creating a mesh of the cutting elements
and blades of the tool, and establishing a coordinate relationship
(coordinate system transformation) between the cutting elements and
the blades, between the blades and the tip of the BHA.
[0085] The third part 218 of the mechanics analysis model 210 of
the drilling tool assembly is a mechanics analysis model of the
drill bit, which takes into account details of selected drill bit
design. The drill bit mechanics analysis model 218 is constructed
by creating a mesh of the cutting elements and cones (for a roller
cone bit) of the bit, and establishing a coordinate relationship
(coordinate system transformation) between the cutting elements and
the cones, between the cones and the bit, and between the bit and
the tip of the BHA.
[0086] Once the (three-part) mechanics analysis model for the
drilling tool assembly is constructed 210 (using Newton's second
law) and wellbore constraints specified, the mechanics model and
constraints can be used to determine the constraint forces on the
drilling tool assembly when forced to the wellbore trajectory and
bottomhole from its original "stress free" state. Such a
methodology is disclosed for example, in U.S. Pat. No. 6,785,641,
which is incorporated by reference in its entirety.
[0087] Once a dynamic response conforming to the borehole wall
constraints is determined (using the methodology disclosed in the
'641 patent for example) for an incremental rotation, the
constraint loads on the drilling tool assembly due to interaction
with the bore hole wall and the bottomhole during the incremental
rotation are determined.
[0088] As noted above, output information from a dynamic simulation
of a drilling tool assembly drilling an earth formation may
include, for example, the drilling tool assembly configuration (or
response) obtained for each time increment, and corresponding bit
forces, cone forces, cutting element forces, impact forces,
friction forces, dynamic WOB, resulting bottomhole geometry, etc.
This output information may be presented in the form of a visual
representation (indicated at 118 in FIG. 5), such as a visual
representation of the borehole being drilled through the earth
formation with continuous updated bottomhole geometries and the
dynamic response of the drilling tool assembly to drilling, on a
computer screen. Alternatively, the visual representation may
include graphs of parameters provided as input and/or calculated
during the simulation, such as lateral and axial displacements of
the tools/bits during simulated drilling.
[0089] For example, a time history of the dynamic WOB or the wear
of cutting elements during drilling may be presented as a graphic
display on a computer screen. It should be understood that the
invention is not limited to any particular type of display.
Further, the means used for visually displaying aspects of
simulated drilling is a matter of convenience for the system
designer, and is not intended to limit the invention.
[0090] The example described above represents only one embodiment
of the invention. Those skilled in the art will appreciate that
other embodiments can be devised which do not depart from the scope
of the invention as disclosed herein. For example, an alternative
method can be used to account for changes in constraint forces
during incremental rotation. For example, instead of using a finite
element method, a finite difference method or a weighted residual
method can be used to model the drilling tool assembly. Similarly,
other methods may be used to predict the forces exerted on the bit
as a result of bit/cutting element interaction with the bottomhole
surface. For example, in one case, a method for interpolating
between calculated values of constraint forces may be used to
predict the constraint forces on the drilling tool assembly.
Similarly, a different method of predicting the value of the
constraint forces resulting from impact or frictional contact may
be used.
[0091] Further, a modified version of the method described above
for predicting forces resulting from cutting element interaction
with the bottomhole surface may be used. These methods can be
analytical, numerical (such as finite element method), or
experimental. Alternatively, methods such as disclosed in SPE Paper
No. 29922 noted above or PCT Patent Application Nos. WO 00/12859
and WO 00/12860 may be used to model roller cone drill bit
interaction with the bottomhole surface, or methods such as
disclosed in SPE papers no. 15617 and no. 15618 noted above may be
used to model fixed-cutter bit interaction with the bottomhole
surface if a fixed-cutter bit is used.
Method of Dynamically Simulating Cutting Tool/Bit
[0092] Some embodiments of the invention provide methods for
analyzing drill string assembly or drill bit vibrations during
drilling. In one embodiment, vibrational forces acting on the bit
and the cutting tool may be considered as frequency response
functions (FRF), which may be derived from measurements of an
applied dynamic force along with the vibratory response motion,
which could be displacement, velocity, or acceleration. For
example, when a vibratory force, f(t), is applied to a mass (which
may be the bit or the hole opener), the induced vibration
displacement, x(t) may be determined. The FRF may be derived from
the solution of the differential equation of motion for a single
degree of freedom (SDOF) system. This equation is obtained by
setting the sum of forces acting on the mass equal to the product
of mass times acceleration (Newton's second law): f .function. ( t
) + c .times. d x .function. ( t ) d t + kx .function. ( t ) = m
.times. d 2 .times. x .function. ( t ) d t 2 ( 1 ) ##EQU1## where:
f(t)=time-dependent force (lb.) x(t)=time-dependent displacement
(in.) m=system mass k=spring stiffness (lb.-in.) c=viscous damping
(lb./in./s)
[0093] The FRF is a frequency domain function, and it is derived by
first taking the Fourier transform of Equation (1). One of the
benefits of transforming the time-dependent differential equation
is that a fairly easy algebraic equation results, owing to the
simple relationship between displacement, velocity, and
acceleration in the frequency domain. These relationships lead to
an equation that includes only the displacement and force as
functions of frequency. Letting F(.omega.) represent the Fourier
transform of force and X(.omega.) represent the transform of
displacement: (-.omega..sup.2m+ic.omega.+k)X(.omega.)=F(.omega.)
(2)
[0094] The circular frequency, .omega., is used here (radians/s).
The damping term is imaginary, due to the 90.degree. phase shift of
velocity with respect to displacement for sinusoidal motion. FRF
may be obtained by solving for the displacement with respect to the
force in the frequency domain. The FRF is usually indicated by the
notation, h(.omega.): h .function. ( .omega. ) = 1 - .omega. 2
.times. m + I .times. .times. c .times. .times. .omega. + k ( 3 )
##EQU2##
[0095] Some key parameters in Equation 3 may be defined as follows:
h .function. ( .omega. ) = ( 1 - .beta. 2 ) - 2 .times. I .times.
.times. .beta. - m .times. .times. .omega. r 2 .function. [ ( 1 -
.beta. 2 ) 2 + 4 .times. .zeta. 2 .times. .beta. 2 ] ( 4 )
##EQU3##
[0096] This form of the FRF allows one to recognize the real and
imaginary parts separately. The new parameters introduced in
Equation (4) are the frequency ratio, .beta.=.omega./.omega..sub.r,
and the damping factor, .xi., wherein .omega..sub.r is the
resonance frequency of the system. The resonance frequency depends
on the system mass and stiffness: .omega. t = k m ( 5 )
##EQU4##
[0097] The above discussion pertains to single degree of freedom
vibration theory. However, in the embodiments discussed herein, the
cutting tools and bit act as a multiple degree of freedom system
(MDOF) having many modes of vibration. The FRF for MDOF can be
understood as a summation of SDOF FRFs, each having a resonance
frequency, damping factor, modal mass, modal stiffness, and modal
damping ratio.
[0098] A matrix of mode coefficients, .PSI..sub.jr, represents all
the mode shapes of interest of a structure. The mode coefficient
index, j, locates a numbered position on the structure (a
mathematical degree of freedom) and the index, r, indicates the
mode shape number. Modes are numbered in accordance with increasing
resonance frequencies. The vector component coordinate
transformation from abstract modal coordinates, X, to physical
coordinates, X, is: {X}=[.PSI.]{X} (6)
[0099] Each column in the [.PSI.]matrix is a list of the mode
coefficients describing a mode shape.
[0100] Now, any system having mass, stiffness and damping
distributed throughout can be represented with matrices. Using
them, a set of differential equations can be written. The frequency
domain form is: [-.omega..sup.2[M]+i.omega.[C]+[K]]{X}={F} (7)
[0101] Displacements and forces at the numbered positions on a
structure appear as elements in column matrices. The mass, damping,
and stiffness matrix terms are usually combined into a single
dynamic matrix, [D]: [D]{X}={F} (8)
[0102] A complete matrix, [H], of FRFs would be the inverse of the
dynamic matrix. Thus, we have the relationship: {X}=[H]{F} (9)
[0103] Individual elements of the [H] matrix are designated with
the notation, h.sub.jk (.omega.), where the j index refers to the
row (location of response measurement) and the k index to the
column (location of force). A column of the [H] matrix may be
obtained experimentally by applying a single force at a numbered
point, k, on the structure while measuring the response motion at
all n points on the structure, j=1,2,3 . . . n. The [H] matrix
completely describes a structure dynamically. A one-time
measurement of the [H] matrix defines the structure for all
time--until a defect begins to develop. Then subtle changes crop up
all over the [H] matrix. From linear algebra we have the
transformation from the [H] matrix in modal coordinates to the
physical [H] matrix. [H]=[.PSI.][H][.PSI.].sup.T (10)
[0104] This provides an understanding of a measured FRF, h.sub.jk
(.omega.), as the superposition of modal FRFs. Equation (10) may be
expanded for any element of the [H] matrix (selecting out a row and
column) to obtain the result: h jk = t = 1 N .times. .PSI. jr
.times. .PSI. kr m r .times. .omega. r 2 .function. [ ( 1 - .beta.
2 ) - 2 .times. I .times. .times. r .times. .beta. r ( 1 - .beta. 2
) 2 + 4 .times. .zeta. r 2 .times. .beta. r 2 ] ( 11 ) ##EQU5##
[0105] In order to fully characterize the system, the distance
between the two or more components (e.g., the drilling tool (hole
opener) and the drill bit) may need to be considered as well as the
coupled nature of the elements. For example, the hole opener and
the bit may be considered to be masses m.sub.1 and m.sub.2 coupled
via a spring. Those having ordinary skill in the art will
appreciate that a number of computational techniques may be used to
determine this interaction, and that no limitation on the scope of
the present invention is intended thereby.
[0106] In another embodiment of the invention, the vibrational,
torsional, axial, and/or lateral forces encountered by the hole
opener and/or bit may be physically measured and stored in a
database. In this embodiment, with respect to the drill bit for
example, as explained in U.S. Pat. No. 6,516,293, a number of
inserts can be tested against various formations of interest to
determine the forces acting on the inserts. These forces may then
be summed to yield the forces acting on the bit.
[0107] Similarly, strain gages, vibrational gages and/or other
devices may be used to determine the force encountered by the bit
or drilling tool under a given set of conditions. Those of ordinary
skill in the art will further appreciate that a combination of
theoretical and experimental approaches may be used in order to
determine the forces acting on the bit and drilling tool (or
tools).
[0108] In some embodiments, the driller may require that an angle
be "built" ("build angle") into the well. A build angle is the rate
that the direction of the longitudinal axis of the well bore
changes, which is commonly measured in degrees per 100 feet. The
extent of the build angle may also be referred to as the "dogleg
severity." Another important directional aspect is the "walk" rate.
The walk rate refers to the change in azimuthal (compass) direction
of the well bore. Control and prediction of the drilling direction
is important for reaching target zones containing hydrocarbons. In
addition, the drop tendency of the bit/secondary cutting structures
may be modeled. In one embodiment, methods in accordance with
embodiments of the present application may be used to match the
drop/walk tendency of a bit with the drop/walk tendency of
secondary cutting structures. Alternatively, the axial locations of
the components may be adjusted to achieve a desired effect on
trajectory.
[0109] For such an embodiment, a drill bit used in accordance with
an embodiment of the present invention may be similar to that
disclosed in U.S. Pat. No. 5,937,958, which is assigned to the
assignee of the present invention, and is incorporated by reference
in its entirety.
[0110] Referring initially to FIGS. 8 and 9, a PDC bit 500
typically comprises a generally cylindrical, one-piece body 810
having a longitudinal axis 811 and a conical cutting face 812 at
one end. Face 812 includes a plurality of blades 821, 822, 823, 824
and 825 extending generally radially from the center of the cutting
face 812. Each blade supports a plurality of PDC cutter elements as
discussed in detail below. As best shown in FIG. 8, cutting face
812 has a central depression 814, a gage portion and a shoulder
therebetween. The highest point (as drawn) on the cutter tip
profiles defines the bit nose 817 (FIG. 9). This general
configuration is well known in the art. Nevertheless, applicants
have discovered that the walking tendencies of the bit can be
enhanced and that a bit that walks predictably and precisely can be
constructed by implementing several novel concepts. These novel
concepts are set out in no particular order below and can generally
be implemented independently of each other, although it is
preferred that at least three be implemented simultaneously in
order to achieve more satisfactory results. A preferred embodiment
of the present invention entails implementation of multiple ones of
the concepts described in detail below. The bit shown in FIGS. 8
and 9 is a 121/4 inch bit. It will be understood that the
dimensions of various elements described below correspond to this
121/4 inch bit and that bits of other sizes can be constructed
according to the same principles using components of different
sizes to achieve similar results.
Active and Passive Zones
[0111] Referring again to FIGS. 8 and 9, the cutting face 812 of a
bit constructed in accordance with the present invention includes
an active zone 820 and a passive zone 840. Active zone 820 is a
generally semi-circular zone defined herein as the portion of the
bit face lying within the radius of nose 817 and extending from
blade 821 to blade 823 and including the cutters of blades 821, 822
and 823. According to a preferred embodiment, active zone 820 spans
approximately 120-180 degrees and preferably approximately 160
degrees. Passive zone 840 is a generally semi-circular zone defined
herein as the portion of the bit face lying within the radius of
nose 817 and extending from blade 824 to blade 825 and including
the cutters of blades 824 and 825. According to a preferred
embodiment, passive zone 840 spans approximately 50-90 degrees and
preferably approximately 60 degrees.
Primary and Secondary Cutter Tip Profiles
[0112] Referring now to FIG. 10, a primary cutter tip profile p
that is used in the active zone and a secondary cutter tip profile
s that is used in the passive zone are superimposed on one another.
While the gage portions 816 of the two blades have similar profiles
up to the bit nose 817, the secondary profile s drops away from the
bit nose 817 more steeply toward the center of face 812 than does
the primary profile p. According to a preferred embodiment, the
tips of the cutters on blades 824 and 825 lying between the bit's
central axis 811 and its nose 817 are located on the secondary
profile s while the tips of the cutters on blades 821, 822, and 823
lying between the bit's central axis 811 and its nose 817 are
located on the primary profile p.
[0113] In general, this difference in profiles means that cutters
toward the center of face 812 in passive zone 840 will contact the
bottom of the borehole to a reduced extent and the cutting will be
performed predominantly by cutters on the primary profile, on
blades 821, 823. For this reason, the forces on cutters on the
primary profile lying in the active zone are greater than the
forces on cutters on the secondary profile lying in the passive
zone. Likewise, the torque generated by the cutters on the primary
profile that lie in the active zone is greater than the torque
generated by the cutters on the secondary profile that lie in the
passive zone. The two conditions described above, coupled with the
fact that the torque on the portion of the bit face that lies
within the radius of nose 817 is greater than the torque generated
in the shoulder and gage portions of cutting surface 812, tend to
cause the bit to walk in a desired manner. The degree to which
walking occurs depends on the degree of difference between the
primary and secondary profiles. As the secondary profile becomes
more steep, the walk tendency increase. In many instances, it will
be desirable to provide a secondary profile that is not overly
steep, so as to provide a bit that walks slowly and in a controlled
manner.
[0114] In an alternative embodiment shown in FIG. 10A, the
secondary cutter tip profile s can be parallel to but offset from
the primary cutter tip profile p. The net effect on the torque
distribution and resultant walking tendencies is comparable to that
of the previous embodiment.
Blade Relationship
[0115] Referring again to FIG. 9, another factor that influences
the bit's tendency to walk is the relationship of the blades and
the manner in which they are arranged on the bit face.
Specifically, the angles between adjacent pairs of blades and the
angles between blades having cutters in redundant positions affects
the relative aggressiveness of the active and passive zones and
hence the torque distribution on the bit. To facilitate the
following discussion, the blade position is used herein to mean the
position of a radius drawn through the last or outermost non-gage
cutter on a blade. According to the embodiment shown in the
Figures, significant angles include those between blades 821 and
823 and between blades 824 and 825. These may be approximately 180
degrees and 60 degrees, respectively. According to an embodiment,
the blades in the passive zone, having redundant cutters, are no
more than 60 degrees apart.
Imbalance Vectors
[0116] In addition to the foregoing factors, a bit in accordance
with embodiments of the present invention may have an imbalance
vector that has a magnitude of approximately 10 to 25 percent of
its weight on bit and more at least 15 percent of its weight on
bit, depending on its size. The imbalance force vector may lie in
the active zone 820 and preferably in the leading half of the
active zone 820. In some embodiments, the imbalance force vector is
oriented as closely as possible to the leading edge of active zone
820 (blade 821). The tendency of a bit to walk increases as the
magnitude of the imbalance force vector increases. Similarly, the
tendency of a bit to walk increases as the imbalance force vector
approaches leading blade 821. The magnitude of the imbalance force
can be increased by manipulating the geometric parameters that
define the positions of the PDC cutters on the bit, such as back
rake, side rake, height, angular position and profile angle.
Likewise, the desired direction of the imbalance force vector can
be achieved by manipulation of the same parameters.
[0117] In other embodiments, the present invention may be used to
model the performance of rotary steerable systems that include both
a bit and a hole opener. Vibrational analysis may be particularly
important in these systems, given the demands and constraints that
such systems are under.
[0118] While reference has been made to a fixed blade hole opener,
those having ordinary skill in the art will recognize that
expandable hole openers may also be used. Exapandable hole openers
are disclosed, for example, in U.S. Pat. No. 6,732,817, which is
assigned to the assignee or the present invention and is
incorporated by reference. In addition, those having ordinary skill
will recognize that concentric or eccentric hole openers may be
used.
[0119] Referring now to FIGS. 11 and 12, an expandable tool which
may be used in embodiments of the present invention, generally
designated as 500, is shown in a collapsed position in FIG. 11 and
in an expanded position in FIG. 12. The expandable tool 500
comprises a generally cylindrical tool body 510 with a flowbore 508
extending therethrough. The tool body 510 includes upper 514 and
lower 512 connection portions for connecting the tool 500 into a
drilling assembly. In approximately the axial center of the tool
body 510, one or more pocket recesses 516 are formed in the body
510 and spaced apart azimuthally around the circumference of the
body 510. The one or more recesses 516 accommodate the axial
movement of several components of the tool 500 that move up or down
within the pocket recesses 516, including one or more moveable,
non-pivotable tool arms 520. Each recess 516 stores one moveable
arm 520 in the collapsed position.
[0120] FIG. 12 depicts the tool 500 with the moveable arms 520 in
the maximum expanded position, extending radially outwardly from
the body 510. Once the tool 500 is in the borehole, it is only
expandable to one position. Therefore, the tool 500 has two
operational positions--namely a collapsed position as shown in FIG.
11 or an expanded position as shown in FIG. 12. However, the spring
retainer 550, which is a threaded sleeve, can be adjusted at the
surface to limit the full diameter expansion of arms 520. The
spring retainer 550 compresses the biasing spring 540 when the tool
500 is collapsed, and the position of the spring retainer 550
determines the amount of expansion of the arms 520. The spring
retainer 550 is adjusted by a wrench in the wrench slot 554 that
rotates the spring retainer 550 axially downwardly or upwardly with
respect to the body 510 at threads 551. The upper cap 555 is also a
threaded component that locks the spring retainer 550 once it has
been positioned. Accordingly, one advantage of the present tool is
the ability to adjust at the surface the expanded diameter of the
tool 500. Unlike conventional underreamer tools, this adjustment
can be made without replacing any components of the tool 500.
[0121] In the expanded position shown in FIG. 12, the arms 520 will
either underream the borehole or stabilize the drilling assembly,
depending upon how the pads 522, 524 and 526 are configured. In the
configuration of FIG. 12, cutting structures 700 on pads 526 would
underream the borehole. Wear buttons 800 on pads 522 and 524 would
provide gauge protection as the underreaming progresses. Hydraulic
force causes the arms 520 to expand outwardly to the position shown
in FIG. 12 due to the differential pressure of the drilling fluid
between the flowbore 508 and the annulus 22.
[0122] The drilling fluid flows along path 605, through ports 595
in the lower retainer 590, along path 610 into the piston chamber
535. The differential pressure between the fluid in the flowbore
508 and the fluid in the borehole annulus 22 surrounding tool 500
causes the piston 530 to move axially upwardly from the position
shown in FIG. 11 to the position shown in FIG. 12. A small amount
of flow can move through the piston chamber 535 and through nozzles
575 to the annulus 22 as the tool 500 starts to expand. As the
piston 530 moves axially upwardly in pocket recesses 516, the
piston 530 engages the drive ring 570, thereby causing the drive
ring 570 to move axially upwardly against the moveable arms 520.
The arms 520 will move axially upwardly in pocket recesses 516 and
also radially outwardly as the arms 520 travel in channels 518
disposed in the body 510. In the expanded position, the flow
continues along paths 605, 610 and out into the annulus 22 through
nozzles 575. Because the nozzles 575 are part of the drive ring
570, they move axially with the arms 520. Accordingly, these
nozzles 575 are optimally positioned to continuously provide
cleaning and cooling to the cutting structures 700 disposed on
surface 526 as fluid exits to the annulus 22 along flow path
620.
[0123] The underreamer tool 500 may be designed to remain
concentrically disposed within the borehole. In particular, the
tool 500 of the present invention preferably includes three
extendable arms 520 spaced apart circumferentially at the same
axial location on the tool 510. In the preferred embodiment, the
circumferential spacing would be 120 degrees apart. This three arm
design provides a full gauge underreaming tool 500 that remains
centralized in the borehole at all times.
[0124] In some embodiments, the simulation provides visual outputs.
In one embodiment, the visual outputs may include performance
parameters. Performance parameters, as used herein may include rate
of penetration (ROP), forces encountered, force imbalance, degree
of imbalance, maximum, minimum, and/or average forces (including
but not limited to vibrational, torsional, lateral, and axial). The
outputs may include tabular data of one or more performance
parameters. Additionally, the outputs may be in the form of graphs
of a performance parameter, possibly with respect to time. A
graphical visualization of the drill bit, drill string, and/or the
drilling tools (e.g., a hole opener) may also be output. The
graphical visualization (e.g., 2-D, 3-D, or 4-D) may include a
color scheme for the drill string and BHA to indicate performance
parameters at locations along the length of the drill string and
bottom hole assembly.
[0125] Visual outputs that may be used in the present invention
include any output shown or described in any of U.S. patent
application Ser. Nos. 09/524,088 (now U.S. Patent No. 6,516,293),
Ser. No. 09/635,116 (now U.S. Pat. No. 6,873,947), Ser. No.
10/749,019, Ser. No. 09/689,299 (now U.S. Pat. No. 6,785,641), Ser.
No. 10/852,574, Ser. No. 10/851,677, Ser. No. 10/888,358, Ser. No.
10/888,446, all of which are expressly incorporated by reference in
their entirety.
[0126] The overall drilling performance of the drill string and
bottom hole assembly may be determined by examining one or more of
the available outputs. One or more of the outputs may be compared
to the selected drilling performance criterion to determine
suitability of a potential solution. For example, a 3-D graphical
visualization of the drill string may have a color scheme
indicating vibration quantified by the sudden changes in bending
moments through the drilling tool assembly. Time based plots of
accelerations, component forces, and displacements may also be used
to study the occurrence of vibrations. Other drilling performance
parameters may also be illustrated simultaneously or separately in
the 3-D graphical visualization. Additionally, the 3-D graphical
visualization may display the simulated drilling performed by the
drilling tool assembly.
Method of Positioning Secondary Cutting Structures
[0127] A method of positioning a secondary cutting structure (in
this case a reamer) is shown in FIG. 13. In this embodiment, a
neutral point of the drill string is determined (or approximated)
(ST 1000). In this application, the neutral point is defined as the
point on a string of tubulars at which there are neither tension
nor compression forces present. Below the neutral point, there will
be compression forces that build toward the bottom of the wellbore.
Above the neutral point, tensile forces build to a maximum applied
at the hanger or as hook load.
[0128] One method of determining the neutral point involves using
the specified drill string, as well as the anticipated weight on
bit, buoyancy factor, wall drag, and hole inclination to calculate
the neutral point. In one embodiment, in order to determine the
neutral point, a graph of axial tension in the drill string versus
depth is created. Those having ordinary skill in the art will
appreciate that the axial tension may be determined by:
F.sub.T=w.sub.dpx.sub.dp+W.sub.2+p.sub.1(A.sub.2-A.sub.1)-p.sub.2A.sub.2--
F.sub.b,
[0129] where w.sub.dp is the weight per foot of drillpipe in air,
x.sub.dp is the distance from the bottom of the drillpipe (top of
drill collars) to the point of interest, p.sub.1 is the hydrostatic
pressure at the top of the drill collars, A.sub.2 is the
cross-sectional area of the drill collars, A.sub.1 is the
cross-sectional area of the drill pipe, p.sub.2 is the hydrostatic
pressure at the bottom of the drill collar, and F.sub.b is the
weight on bit.
[0130] Based on this equation, a graph of axial tension versus
depth may be created. However, this equation neglects the effect of
buoyancy caused by the use of well fluid. To account for this, a
stability force is also calculated. The stability force is defined
by: F.sub.s+=A.sub.ip.sub.i-A.sub.op.sub.o
[0131] where A.sub.i is the cross-sectional area computed using the
inside pipe diameter, d, and the A.sub.o is the cross-sectional
area using the outside diameter of the pipe d.sub.n. The stability
force is then plotted on a tension versus depth graph, and the
intersection of the axial compression force and the stability force
is the neutral point of the system.
[0132] Those having ordinary skill in the art will also appreciate
that specific commercial tools exist for measuring the neutral
point of a system exist. Thus, in other embodiments, rather than
determining the neutral point by calculation, physical measurement
of the neutral point may be made.
[0133] After determining the neutral point, a model for the hole
enlargement system (which include a drill bit and a secondary
cutting structure) and the well bore is created using input
parameters. The input parameters may include drilling tool assembly
design parameters, well bore parameters, and/or drilling operating
parameters. Those having ordinary skill in the art will appreciate
that other parameters may be used as well.
[0134] Examples of drilling tool assembly design parameters include
the type, location, and number of components included in the
drilling tool assembly; the length, ID, OD, weight, and material
properties of each component; the type, size, weight,
configuration, and material properties of the drill bit; and the
type, size, number, location, orientation, and material properties
of the cutting elements on the drill bit. Material properties in
designing a drilling tool assembly may include, for example, the
strength, elasticity, and density of the material. It should be
understood that drilling tool assembly design parameters may
include any other configuration or material parameter of the
drilling tool assembly without departing from the scope of the
invention.
[0135] Well bore parameters typically include the geometry of a
well bore and formation material properties. The trajectory of a
well bore in which the drilling tool assembly is to be confined
also is defined along with an initial well bore bottom surface
geometry. Because the well bore trajectory may include either
straight, curved, or a combination of straight and curved sections,
well bore trajectories, in general, may be defined by parameters
for each segment of the trajectory. For example, a well bore may be
defined as comprising N segments characterized by the length,
diameter, inclination angle, and azimuth direction of each segment
and an indication of the order of the segments (i.e., first,
second, etc.). Well bore parameters defined in this manner may then
be used to mathematically produce a model of the entire well bore
trajectory. Formation material properties at various depths along
the well bore may also be defined and used. One of ordinary skill
in the art will appreciate that well bore parameters may include
additional properties, such as friction of the walls of the well
bore and well bore fluid properties, without departing from the
scope of the invention.
[0136] Drilling operating parameters typically include the rotary
table (or top drive mechanism), speed at which the drilling tool
assembly is rotated (RPM), the downhole motor speed (if a downhole
motor is included) and the hook load. Furthermore, drilling
operating parameters may include drilling fluid parameters, such as
the viscosity and density of the drilling fluid, for example. It
should be understood that drilling operating parameters are not
limited to these variables. In other embodiments, drilling
operating parameters may include other variables (e.g. rotary
torque and drilling fluid flow rate). Additionally, for the purpose
of drilling simulation, drilling operating parameters may further
include the total number of drill bit revolutions to be simulated
or the total drilling time desired for drilling simulation. Once
the parameters of the system (i.e., drilling tool assembly under
drilling conditions) are defined, they may be used with various
interaction models to simulate the dynamic response of the drilling
tool assembly drilling earth formation as described below.
[0137] After the hole enlargement system has been modeled, the
system is simulated using the techniques described above (ST 1010).
The simulation may be run, for example, for a selected number of
drill bit rotations, depth drilled, duration of time, or any other
suitable criteria.
[0138] After completion of the simulation, performance parameter(s)
are output (ST 1020). Examples of performance parameters include
rate of penetration (ROP), rotary torque required to turn the
drilling tool assembly, rotary speed at which the drilling tool
assembly is turned, drilling tool assembly lateral, axial, or
torsional vibrations induced during drilling, weight on bit (WOB),
forces acting on components of the drilling tool assembly, and
forces acting on the drill bit and components of the drill bit
(e.g., on blades, cones, and/or cutting elements). Drilling
performance parameters may also include the inclination angle and
azimuth direction of the borehole being drilled. One skilled in the
art will appreciate that other drilling performance parameters
exist and may be considered without departing from the scope of the
invention.
[0139] After the performance parameter has been output, the axial
location of the secondary cutting structure is adjusted to move the
secondary cutting structure closer to the calculated neutral point.
The simulation is repeated, and the effect on performance
parameter(s) reviewed. The present inventors have advantageously
discovered that by locating a secondary cutting structure (such as
a reamer) adjacent (or at least closer than originally located) to
the neutral point of the system, a more stable system can be
achieved. In particular the dynamic response of the system is
improved. This can result in extended drilling life for components
used in the system.
[0140] Thus, in one embodiment, given a proposed system, and
operating parameters, one can determine preferred locations for the
reamer (or similar component) and this can be proposed or passed to
an operator or driller as a proposed drilling system to be used in
the given application.
[0141] In an alternative embodiment of the present invention, given
a fixed system, a range of neutral points may be determined using a
range of weight on bit (WOB) inputs. As a result, a preferred, or
useful, range of WOB, may be provided to a driller, which positions
the neutral point adjacent the secondary cutting structure.
EXAMPLE
[0142] In one exemplary embodiment, the effect of positioning a
reamer adjacent to the neutral point of a drill string was
investigated. Specifically, the effect of reamer position on a
121/4'' PDC bit having 9 blades and 16 mm & 13 mm cutters used
in a formation having a compressive strength of 7,000 psi was
investigated. Those having ordinary skill in the art will
appreciate that any drill bit or multiple bits may be modeled. In
the particular example, the weight on bit was 25,000 lbs and the
bit was rotated at 160 rpm. This particular example was in an
inclined well, and a rotary steerable tool was modeled as well. In
addition, in this particular example, a measurement-while-drilling
(MWD) tool was present in the system at a location of 52 feet from
the bit. Those having ordinary skill in the art will appreciate
that a number of other tools may be used while drilling a well, and
their locations and/or cutting structures associated therewith may
be modeled as part of an analysis. In addition, depending on the
system used to drill a well, various locations may be occupied,
providing a constraint on the locations of the one or more
secondary cutting structures.
[0143] As a first step, the neutral point of the system was
determined to be approximately 161 feet away from the bit. The
effect on the system was then modeled with a reamer located 80
feet, 104 feet, 131 feet, and 161 feet away from the bit. FIG. 14,
the effect of reamer placement on the lateral acceleration of the
reamer was investigated. As can be seen from the figure, by moving
the reamer closer to (more adjacent) to the neutral point, the
lateral acceleration at the reamer is significantly reduced, which
may improve the performance of the entire drilling system.
[0144] Next, torque oscillations at both the bit and the reamer
were investigated as a function of reamer placement. FIGS. 15A-15D
show the effect of moving the reamer 80 feet from the bit, 104 feet
from the bit, 131 feet from the bit, and 161 feet from the bit
(i.e., at the neutral point). As can be seen from the figures, by
moving the reamer closer to the neutral point, a lessening of
torque oscillations is seen. The overall drilling performance of
the system may be improved. It should be noted that depending on
the particular application, and the constraints of the system,
moving one or more secondary cutting structures (such as the reamer
in this example) may involve placing the reamer at or near the
neutral point. However, in other embodiments, moving one or more
secondary structures adjacent to the neutral point may involve only
a movement of several feet, as satisfactory performance gain may be
seen, or other design constraints may be controlling.
[0145] The effect of reamer position on torque at the bit, reamer,
and at the rotary table (i.e., surface torque) is shown in FIG. 16.
As shown in that Figure, by moving the reamer towards the neutral
point, the overall torque performance of the system may be
improved.
[0146] In FIG. 17, the effect on rate of penetration for the reamer
was simulated as a function of distance from the bit. As can be
seen in the figure, the highest rate of penetration was achieved
when positioning the reamer at the neutral point.
[0147] In FIG. 18, the bending moment at the MWD tool (which is
located at 52 feet) is simulated as function of reamer location. As
can be seen in the figure the bending moments are relatively lower
and more constant when the reamer is located at 161 feet when
compared with positions closer to the drill bit. Thus, location of
the reamer may also effect secondary components, not just secondary
and primary cutting structures. Embodiments disclosed herein may be
used to model the effect of reamer (or other cutting structures) on
secondary components such as motors, MWD tools, LWD tools, sampling
probes, or other components known to those having ordinary skill in
the art.
[0148] Thus, embodiments of the present invention provide
techniques for locating secondary cutting structures in a drill
string. In selected embodiments a secondary cutting structure may
comprise a reamer. The reamer may be located at the neutral point,
within 5 feet of the neutral point, within 10 feet of the neutral
point, within 20 feet of the neutral point, within 30 feet of the
neutral point, within 50 feet of the neutral point, within 60 feet
of the neutral point, or within 100 feet of the neutral point,
depending on the selected embodiment.
[0149] Specifically, selected embodiments involve determining
(whether by calculating or by other means) a neutral point of a
drilling system, and positioning a secondary cutting structure
adjacent to the neutral point of the drilling system.
[0150] While the invention has been described with respect to a
limited number of embodiments, those skilled in the art, having
benefit of this disclosure, will appreciate that other embodiments
can be devised which do not depart from the scope of the invention
as disclosed herein. Accordingly, the scope of the invention should
be limited only by the attached claims.
* * * * *